Flow-level network model

A flow-level model treats each document transfer as a flow whose rate depends on the current occupancy and resource capacities. With independent Poisson processes for arrivals and independent unit-mean exponential distributions for sizes, a route's total completion rate equals its allocated aggregate service.

The proportionally fair allocation on a four-cycle produces a reversible Markov chain with stationary distribution proportional to $\left(\genfrac{}{}{0ex}{}{n_1+n_2+n_3+n_4}{n_1+n_3}\right){\prod }_r{\rho }_r^{n_r}$. This is normalizable exactly when every resource's offered load is strictly below capacity, equivalently $\max ({\rho }_1,{\rho }_3)+\max ({\rho }_2,{\rho }_4)<1$.